Author | Humphreys, James E. author |
---|---|
Title | Introduction to Lie Algebras and Representation Theory [electronic resource] / by James E. Humphreys |
Imprint | New York, NY : Springer New York, 1972 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-6398-2 |
Descript | XIII, 173 p. online resource |
I. Basic Concepts -- 1. Definitions and first examples -- 2. Ideals and homomorphisms -- 3. Solvable and nilpotent Lie algebras -- II. Semisimple Lie Algebras -- 4. Theorems of Lie and Cartan -- 5. Killing form -- 6. Complete reducibility of representations -- 7. Representations of sl (2, F) -- 8. Root space decomposition -- III. Root Systems -- 9. Axiomatics -- 10. Simple roots and Weyl group -- 11. Classification -- 12. Construction of root systems and automorphisms -- 13. Abstract theory of weights -- IV. Isomorphism and Conjugacy Theorems -- 14. Isomorphism theorem -- 15. Cartan subalgebras -- 16. Conjugacy theorems -- V. Existence Theorem -- 17. Universal enveloping algebras -- 18. The simple algebras -- VI. Representation Theory -- 20. Weights and maximal vectors -- 21. Finite dimensional modules -- 22. Multiplicity formula -- 23. Characters -- 24. Formulas of Weyl, Kostant, and Steinberg -- VII. Chevalley Algebras and Groups -- 25. Chevalley basis of L -- 26. Kostantโs Theorem -- 27. Admissible lattices -- References -- Afterword (1994) -- Index of Terminology -- Index of Symbols